Prove the following by using the principle of mathematical induction for all `n in N`:`1^2+3^2+5^2+...+(2n-1)^2=(n(2n-1)(2n+1))/3`

Explanation

Let `P (n)` be the given statement.


i.e.,` P (n) : 1^2 + 3^2+ 5^2+ .... + (2n - 1)^2 = [n (2n - 1)(2n + 1)]/3`


For `n = 1,`



`P (1) : 1^2 = [1 (2.1 - 1)(2.1 + 1)]/3`
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